I am doing some calculations in the Standard Model. I have a question that seems rather simple but makes me think a lot. I want to compute the cross section of the following process at the leading order $$ \mu^+\mu^-\rightarrow hh. $$ This can be interesting for a mu-collider. The Feynman diagram I can consider has an intermediate higgs particle decaying into a couple of higgs particles (this vertex exists in the Standard Model) while a $Z^0$ is excluded due to conservation of angular momentum. Is this analysis correct? Otherwise, what is the right Feynman diagram? Also references could be part of a good answer.
You must also take in account the diagram where a muon is the intermediate state, although it is not dominant. This particle will connect the two Higgs vertices.